Related papers: Response and Sensitivity Using Markov Chains
Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing…
In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
We consider the important problem of estimating parameter sensitivities for stochastic models of reaction networks that describe the dynamics as a continuous-time Markov process over a discrete lattice. These sensitivity values are useful…
We investigate the stability of quantum Markov processes with respect to perturbations of their transition maps. In the first part, we introduce a condition number that measures the sensitivity of fixed points of a quantum channel to…
In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems…
Even if a linear system of ordinary differential equations has a globally attracting equilibrium at the origin, small disturbances from the equilibrium may lead to large transient excursions before the system stabilizes. This…
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local…
Data-driven convective parameterization aims to accurately represent convective adjustments to large-scale forcings in a computationally economic manner. While previous studies have demonstrated success using various model architectures,…
Understanding how systems respond to external perturbations is fundamental to statistical physics. For systems far from equilibrium, a general framework for response remains elusive. While progress has been made on the linear response of…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
A semiclassical theory of linear response in finite Fermi systems, based on the Vlasov equation, and its applications to the study of isoscalar vibrations in heavy nuclei are reviewed. It is argued that the Vlasov equation can be used to…
A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter the resulting structure is worked out…
Reaction-diffusion models are widely used to study spatially-extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…
The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these…
We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a…
This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…